{% extends 'homepage.html' %}
{% block content %}

<p>
L-functions associated to {{ KNOWL('character.dirichlet', title='Dirichlet characters') }} are called 
{{ KNOWL('lfunction.dirichlet', title='Dirichlet L-functions') }}.
These L-functions have a {{ KNOWL('lfunction.functional_equation', title='functional equation')}} of the form 
\[
\Lambda(s,\chi) = q^{s/2} \Gamma_{\mathbb R} (s+a) L(s,\chi) = \varepsilon_\chi \Lambda(1-s,\overline{\chi}),
\]
where $q$ is the conductor of $\chi$ and $a$ is 1 (or 0) when $\chi$ is odd (or even).
</p>
<p>
The plot below shows the {{ KNOWL('character.dirichlet.primitive', title='primitive characters') }} 
arranged by the {{ KNOWL('character.dirichlet.conductor', title='conductor') }} and the
{{ KNOWL('character.dirichlet.order', title='order') }} of the character,
with color indicating the {{ KNOWL('character.dirichlet.parity', title='parity')}} of the 
Dirichlet character.  Clicking on an entry will 
take you to the associated Dirichlet L-function.
</p>

<form> 
  <p>
    Conductor range: <span id="modRange"></span>
     </p><div class="slider" id="slider-modulus"></div>
  <p></p>
</form>

{{contents[0]|safe}}


<script type="text/javascript">
  $(function() {

  $("#slider-modulus").slider({
    range: true,
    min: 1,
    max: 50,
    step: 1,
    values: [ {{minModDefault}}, {{maxModDefault}} ],
    slide: function( event, ui ) {
      $("#modRange" ).text( ui.values[ 0 ] + " - " + ui.values[ 1 ] );
    },
    change: function( event, ui ) {
      $("#modRange" ).text( ui.values[ 0 ] + " - " + ui.values[ 1 ] );
      $("#charGraph").attr( 'src', '/browseGraphChar/?min_cond=' + ui.values[ 0 ] + '&max_cond=' + ui.values[ 1 ] + '&max_order=' + {{maxOrder}} + '&min_order=1');
      $("#charGraph").attr( 'height', 60 + 30 * (ui.values[ 1 ]-ui.values[ 0 ]+1));
    }
  });

  $( "#modRange" ).text({{minModDefault}} + " - " + {{maxModDefault}});

  });
</script>
{% endblock %}
